Ag is tangent to circle f at point a. if m< gac = 75, mad = 52 and mab = 88, find m< dec

The complete question in the attached figure

we know that

step 1
find the measure of arc AC
we know that
The inscribed angle measures half of the arc it comprises.
so
m∠GAC=(1/2)*[arc AC]
m∠GAC=75°
(1/2)*arc AC=75°-----> arc AC=150°

step 2
find the arc DC
arc AC=arc AD+arc DC
arc DC=arc AC-arc AD----> arc DC=150°-52°----> arc DC=98°

step 3
find m∠DEC

we know that
The measure of the interior angle is the half-summit of the arcs that comprise it and its opposite.
so
m∠DEC=(1/2)*[arc AB+arc DC]
    
arc AB=88°
arc DC=98°

m∠DEC=(1/2)*[88+98]-----> 
m∠DEC=93°

the answer is
m∠DEC=93°

The distance from point a to point c across the coordinate plane is aproxamatly 8.94 rounded to the nearest hundredth. you use a^2 + b^2 =c^2